Meanwhile, heat olive oil over medium heat in a medium skillet and add leeks and celery. Cook, stirring, until they begin to soften, about 3 minutes, and stir in minced garlic. Cook, stirring, until fragrant, 30 seconds to a minute, and add tomatoes. Season to taste with salt and pepper. Cook, stirring often, until tomatoes have cooked down slightly, about 10 minutes.

Stir leek and tomato mixture into beans, along with summer squash. Bring back to a simmer and cook 15 minutes, until beans are creamy-tender but intact and the vegetables are soft and fragrant. Taste and adjust seasonings. Remove bouquet garni.

Ladle ragout into wide bowls. Top each serving with a generous sprinkling of slivered basil leaves and a spoonful of Parmesan.